Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version
8th Edition
ISBN: 9781119080701
Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein
Publisher: WILEY
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Chapter 2.6, Problem 54P
To determine
The depth of the water in the right tank
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Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank
A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each
tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of
6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,
initially, tank A contains pure water and tank B contains 20 kg of salt.
A
6 L/min
0.2 kg/L
x(t)
100 L
4 L/min
x(0) = 0 kg
3 L/min
B
y(t)
100 L
y(0) = 20 kg
2 L/min
1 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t > 0:
Analytically (hand calculations)
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m₂ = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
www.m
k₁ = 3
(y₁ = 0).
m₁ = 1
k2=2
(y₂ = 0)
|m₂ = 1
Y2
y 2
System in
static
equilibrium
(Net change in
spring length
=32-31)
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁(t) and y₂(t) for the two masses m₁ and m₂ respectively:
Analytically (hand calculations)
100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin N/m. If the mass-spring system has mass m = 2 kg and a
damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is
subjected to the harmonic external force f(t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
Analytically (hand calculations)
Chapter 2 Solutions
Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version
Ch. 2.3 - Prob. 1PCh. 2.3 - The deepest known spot in the oceans is the...Ch. 2.3 - A closed tank is partially filled with glycerin....Ch. 2.3 - A 3-m-diameter vertical cylindrical tank is filled...Ch. 2.3 - Blood pressure is usually given as a ratio of the...Ch. 2.3 - An unknown immiscible liquid seeps into the bottom...Ch. 2.3 - A 30-ft-high downspout of a house is clogged at...Ch. 2.3 - How high a column of SAE 30 oil would be required...Ch. 2.3 - Bathyscaphes are capable of submerging to great...Ch. 2.3 - The deepest known spot in the oceans is the...
Ch. 2.3 - A submarine submerges by admitting seawater (S =...Ch. 2.3 - Determine the pressure at the bottom of an open...Ch. 2.3 - In a certain liquid at rest, measurements of the...Ch. 2.3 - Because of elevation differences, the water...Ch. 2.3 - Under normal conditions the temperature of the...Ch. 2.3 - Often young children drink milk (ρ = 1030 kg/m3)...Ch. 2.3 - (See The Wide World of Fluids article titled...Ch. 2.4 - What would be the barometric pressure reading, in...Ch. 2.4 - Denver, Colorado, is called the “mile-high city”...Ch. 2.4 - Prob. 20PCh. 2.4 - Pikes Peak near Denver, Colorado, has an elevation...Ch. 2.4 - Equation 2.12 provides the relationship between...Ch. 2.4 - As shown in Fig. 2.6 for the U.S. standard...Ch. 2.4 - (See The Wide World of Fluids article titled...Ch. 2.5 - On a given day, a barometer at the base of the...Ch. 2.5 - Aneroid barometers can be used to measure changes...Ch. 2.5 - Bourdon gages (see Video V2.4 and Fig. 2.13) are...Ch. 2.5 - On the suction side of a pump, a Bourdon pressure...Ch. 2.5 - A Bourdon pressure gage attached to the outside of...Ch. 2.6 - Obtain a photograph/image of a situation in which...Ch. 2.6 - A U-tube manometer is used to check the pressure...Ch. 2.6 - A barometric pressure of 29.4 in. Hg corresponds...Ch. 2.6 - For an atmospheric pressure of 101 kPa (abs)...Ch. 2.6 - The closed tank of Fig. P.2.34 is filled with...Ch. 2.6 - A mercury manometer is connected to a large...Ch. 2.6 - The U-tube manometer shown in Fig. P2.36 has two...Ch. 2.6 - A U-tube manometer is connected to a closed tank...Ch. 2.6 - The container shown in Fig. P2.38 holds 60 °F...Ch. 2.6 - A closed cylindrical tank filled with water has a...Ch. 2.6 - Two pipes are connected by a manometer as shown in...Ch. 2.6 - Find the percentage difference in the readings of...Ch. 2.6 - A U-tube manometer is connected to a closed tank...Ch. 2.6 - For the inclined-tube manometer of Fig. P2.43, the...Ch. 2.6 - A flowrate measuring device is installed in a...Ch. 2.6 - The sensitivity Sen of the micromanometer shown in...Ch. 2.6 - The cylindrical tank with hemispherical ends shown...Ch. 2.6 - Determine the elevation difference. Δh, between...Ch. 2.6 - What is the specific gravity of the liquid in the...Ch. 2.6 - For the configuration shown in Fig. P2.49 what...Ch. 2.6 - The manometer shown in Fig. P2.50 has an air...Ch. 2.6 - The U-tube manometer shown in Fig. P2.51 has legs...Ch. 2.6 - Both ends of the U-tube mercury manometer of Fig....Ch. 2.6 - The inverted U-tube manometer of Fig. P2.53...Ch. 2.6 - An inverted U-tube manometer containing oil (SG =...Ch. 2.6 - The sensitivity Sen of the manometer shown in Fig....Ch. 2.6 - In Fig. P2.56 pipe A contains gasoline (SG = 0.7),...Ch. 2.6 - The mercury manometer of Fig. P2.57 indicates a...Ch. 2.6 - Consider the cistern manometer shown in Fig....Ch. 2.6 - Prob. 59PCh. 2.6 - Prob. 60PCh. 2.6 - Determine the new differential reading along the...Ch. 2.6 - Prob. 62PCh. 2.6 - Determine the ratio of areas, A1/A2, of the two...Ch. 2.6 - Prob. 64PCh. 2.6 - Prob. 65PCh. 2.6 - An inverted hollow cylinder is pushed into the...Ch. 2.8 - Obtain a photograph/image of a situation in which...Ch. 2.8 - The basic elements of a hydraulic press are shown...Ch. 2.8 - The hydraulic cylinder shown in Fig. P2.69, with a...Ch. 2.8 - A Bourdon gage (see Fig. 2.13 and Video V2.4) is...Ch. 2.8 - A bottle jack allows an average person to lift one...Ch. 2.8 - Suction is often used in manufacturing processes...Ch. 2.8 - A piston having a cross-sectional area of 0.07 m2...Ch. 2.8 - Prob. 74PCh. 2.8 - The container shown in Fig. P2.75 has square cross...Ch. 2.8 - Find the weight W needed to hold the wall shown in...Ch. 2.8 - Determine the magnitude and direction of the force...Ch. 2.8 - An automobile has just dropped into a river. The...Ch. 2.8 - Consider the gate shown in Fig. P2.79. The gate is...Ch. 2.8 - Will the gate in Problem 44 ever open?
Ch. 2.8 - A tank contains 6 in. of oil (S = 0.82) above 6...Ch. 2.8 - A structure is attached to the ocean floor as...Ch. 2.8 - Concrete is poured into the forms as shown in Fig....Ch. 2.8 - A long, vertical wall separates seawater from...Ch. 2.8 - Forms used to make a concrete basement wall are...Ch. 2.8 - While building a high, tapered concrete wall,...Ch. 2.8 - A homogeneous, 4-ft-wide, 8-ft-long rectangular...Ch. 2.8 - A gate having the shape shown in Fig. P2.88 is...Ch. 2.8 - A pump supplies water under pressure to a large...Ch. 2.8 - Prob. 90PCh. 2.8 - Prob. 91PCh. 2.8 - The dam shown in Fig. P2.92 is 200 ft long and is...Ch. 2.8 - Prob. 93PCh. 2.8 - Figure P2.94 is a representation of the Keswick...Ch. 2.8 - The Keswick dam in Problem 2.94 is made of...Ch. 2.8 - The Keswick dam in Problem 2.94 is made of...Ch. 2.8 - Prob. 97PCh. 2.8 - Prob. 98PCh. 2.8 - Find the magnitude and location of the net...Ch. 2.8 - Prob. 100PCh. 2.8 - Find the total vertical force on the cylinder...Ch. 2.8 - A 3-m-wide, 8-m-high rectangular gate is located...Ch. 2.8 - A gate having the cross section shown in Fig....Ch. 2.8 - The massless, 4-ft-wide gate shown in Fig. P2.104...Ch. 2.8 - A 200-lb homogeneous gate 10 ft wide and 5 ft long...Ch. 2.8 - An open tank has a vertical partition and on one...Ch. 2.8 - Prob. 107PCh. 2.8 - A 4-ft by 3-ft massless rectangular gate is used...Ch. 2.8 - A thin 4-ft-wide, right-angle gate with negligible...Ch. 2.8 - The closed vessel of Fig. P2.110 contains water...Ch. 2.8 - (See The Wide World of Fluids article titled “The...Ch. 2.10 - Obtain a photograph/image of a situation in which...Ch. 2.10 - Prob. 113PCh. 2.10 - Prob. 114PCh. 2.10 - Figure P2.115 shows a cross section of a submersed...Ch. 2.10 - The container shown in Fig. P2.116 has circular...Ch. 2.10 - The 18-ft-long lightweight gate of Fig. P2.117 is...Ch. 2.10 - The air pressure in the top of the 2-liter pop...Ch. 2.10 - In drilling for oil in the Gulf of Mexico, some...Ch. 2.10 -
Hoover Dam (see Video 2.5) is the highest...Ch. 2.10 - A plug in the bottom of a pressurized tank is...Ch. 2.10 -
The homogeneous gate shown in Fig. P2.122...Ch. 2.10 - The concrete (specific weight = 150 lb/ft3)...Ch. 2.10 - Prob. 124PCh. 2.10 - Find the magnitude, direction, and location of the...Ch. 2.10 - A 10-m-long log is stuck against a dam, as shown...Ch. 2.10 - Prob. 127PCh. 2.10 - Prob. 128PCh. 2.10 - Prob. 129PCh. 2.10 - Prob. 130PCh. 2.10 - Prob. 131PCh. 2.11 - Prob. 132PCh. 2.11 - An iceberg (specific gravity 0.917) floats in the...Ch. 2.11 - Prob. 134PCh. 2.11 - Prob. 135PCh. 2.11 - Prob. 136PCh. 2.11 - Prob. 137PCh. 2.11 - Prob. 138PCh. 2.11 - Estimate the minimum water depth needed to float a...Ch. 2.11 - Prob. 140PCh. 2.11 - Prob. 141PCh. 2.11 - Prob. 142PCh. 2.11 - Prob. 143PCh. 2.11 - A solid cylindrical pine (S = 0.50) spar buoy has...Ch. 2.11 - Prob. 145PCh. 2.11 - Prob. 146PCh. 2.11 - Prob. 147PCh. 2.11 - A submarine is modeled as a cylinder with a length...Ch. 2.12 - Prob. 149PCh. 2.12 - Prob. 150PCh. 2.12 - Prob. 151PCh. 2.12 - Prob. 152PCh. 2.12 - Prob. 153PCh. 2.12 - The cylinder in Fig. P2.154 accelerates to the...Ch. 2.12 - A closed cylindrical tank that is 8 ft in diameter...Ch. 2.12 - The cart shown in Fig. P2.156 measures 10.0 cm...Ch. 2.12 - The U-tube manometer in Fig. P2.157 is used to...Ch. 2.12 - Prob. 158PCh. 2.12 - An open 1-m-diameter tank contains water at a...Ch. 2.12 - Prob. 160PCh. 2.12 - Prob. 161PCh. 2.12 - Prob. 162PCh. 2.12 - Prob. 163P
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